I use an old syringe filled with sewing machine oil. Talk nicely to your doctor/nurse and they will usually oblige when you explain what you want it for. As jock1e said earlier, there is normally a sticky label over the front of the fan, just peel back and "inject" !

The label on the fan hub,peeled back reveals a 'well' into which a mere drip of oil is dropped and label replaced.

Which oil, as mentioned 3in1,sewing m/c,

Many years ago a 'Tiny' owner ( remember them?) Had same proplem,the engineer called' went out to his vehicle and came back with the engine dip stick held in a rag and applied the magic drip.
Don't use WD40 however, it dries out will make this NHS worse.

Identified that the main source of noise is the PSU Fan. There are some considerable voltages in that box(very few amps though, I believe), so am wary about taking it apart to oil the fan. Any thoughts and advice welcome on that one.

While I was in there I gave it a wee clean (not much dust) and put a drip of oil on the CPU Fan. However, when I stripped back the cover, it disintegrated. I was going to put a little Sellotape in place of the cover, but then decided to put everything back, sans cover, and ask here as to what is the best course of action.